The Dynamic Programming Algorithm (DPA) was developed in the fifties. However, it is sometimes still used nowadays in various fields because it can easily find the global optimum in certain optimization problems. DPA has been applied to problems of one, two or three dimensions. When the dimension of the problem solved by DPA is equal to one the complexity of the algorithm is polynomial but if the size is greater than one, the complexity becomes NP complete. In such cases a practical implementation of the algorithm is possible only using some approximation. In this paper we present a novel approximation of the two-dimensional Dynamic Programming Algorithm (2D-DPA) with polynomial complexity. We then describe a parallel implementation of the algorithm on a recent Graphics Processing Unit (GPU).
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